Twin-roll casting (TRC) is a near-net shape manufacturing process that is used to produce strips of steel and other metals. During the process, molten metal is poured onto the surface of two casting rolls that simultaneously cool and solidify the metal into a strip at close to its final thickness. As the rolls rotate, angular variations in the shape and thermodynamic characteristics of the rolls can create periodic disturbances in the strip's thickness profile. One example of this is when one side of the strip is inadvertently cast thicker than the other due to a change in the relative gap distance between the rolls' edges. This disturbance is called a wedge, and its presence compromises the quality of the final strip. Compensating for this kind of disturbance, however, is complicated by the presence of large delays between the casting and the measurement of the strip.
In the past, researchers have focused on the stability of the TRC process as well as improving its overall performance. Specifically, many researchers have analyzed the interactions between various process parameters as well as how those interactions affect the steady-state behavior of the process. However, little to no work has been done to address the disturbances that occur on a per-revolution basis. Without addressing these disturbances, many of the steady-state simulations that previous authors have derived, will not be able to achieve the thickness performance objectives that they have outlined.
Due to the rotational nature of TRC, the most prominent dynamics of the roll are periodic. This makes learning-based control algorithms a desirable method for addressing the per-revolution disturbances. Iterative learning control (ILC) is a popular control technique for eliminating periodic disturbances that occur in repetitive processes. Iterative learning control leverages the repeatability of a process to eliminate the influence of periodic disturbances from the process. Originally proposed in the 1980s, ILC has been used to improve the tracking performance of a wide variety of systems in the areas of robotics, chemical processing, and manufacturing. An ILC algorithm uses the error signal(s) from the previous trials, or roll revolutions in this case, to generate modifications to the input signal that will be applied during the next trial.
Many ILC algorithms assume that there are no time delays within the process. In real-world applications, however, this is not always true. Researchers have previously developed ILC algorithms to compensate for time delays that occur within a single iteration of the process. It is shown that, under the assumptions that the delay time is fixed and that the length of the delay is less than the length of one iteration, convergence is guaranteed for small time delay estimation errors. However, these algorithms do not extend to the case of time delays that that are actually multiple iterations in length, as is the case in a variety of applications, including twin-roll steel casting. Nor do they consider the case in which the time delay is time-varying.
Due to the rotational nature of twin roll strip casting, many of the disturbances can be expressed as a function of the rotational position of the casting rolls. Due to numerous physical limitations, however, strip characterization sensors are not co-located with system actuators. As a result, time delays may exceed the duration of a single iteration of the process, i.e., one complete rotation of the casting rolls. This means that an accurate time delay estimate is needed before these measurements can be used in conjunction with feedback algorithms to control the process.
To account for the variability of the time delay, a time delay estimation algorithm is needed. The most common time delay estimation algorithms use correlation-based methods to estimate the time delay within a process. The periodicity of a process, however, makes correlation-based methods unreliable, especially when the delay is multiple periods in length. This is because the periodicity causes the correlation function to have a local maximum for every period within the search window.